The Kloster is a monastery located inside a city.
In Darklands, every city has a Kloster.

Activities

Offer money for prayers

This option will restore some Divine Favor, in exchange for the mentioned payment.

Inquire about tutoring

If successful, this option will allow you to train/study the following skills at the local inn: Religion, Speak Latin, Read & Write.

Study about saints

Each Kloster offers knowledge about 4 saints (fixed from the start of the game). If the inquiry is successful, you can select 1 party member and 1 of the 4 saints; for the indicated payment, that party member will gain permanent knowledge of that saint.
This process always seems to end at Vespers 18, regardless of the time it was started; start learning shortly before this time of the day to save time.

Seek aid in healing wounds

Like the town physician, the Kloster can help in healing the party members' injuries (i.e. restore strength). However, significant virtue is required for a fair chance of success with this option.

Seek sanctuary

Significant virtue is required for a fair chance of success with this option.